{"paper":{"title":"Modifications of CMB Temperature and Polarization Quadrupole Signals in Thurston Spacetimes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Thurston spacetimes generate distinct time-evolving quadrupole patterns in CMB temperature and polarization via Stokes parameters.","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Rajib Saha, Sukanta Panda, Tanay Gupta","submitted_at":"2026-05-14T08:43:08Z","abstract_excerpt":"Recent cosmological tests have discovered a fresh new set of anomalies in the large-scale isotropy of the universe. Motivated thus by the numerous pieces of evidence for large-scale cosmic isotropy violation with the advent of the 'precision cosmology' era, we are led to explore the viability of anisotropic Thurston geometries, described in William Thurston's geometrization conjecture. In this work, we examine the coherent temperature and polarization signals generated in the CMB sky by such geometries. We begin with introducing Thurston spacetimes as our background model and the formalism we "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show the evolution of temperature and polarization amplitudes in terms of such Stokes parameters at different timestamps and attempt to isolate individual Thurston geometries.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That Thurston spacetimes can be used as viable background geometries for the universe while producing coherent, distinguishable CMB signals without additional assumptions about initial conditions or matter content in the anisotropic setting.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Thurston spacetimes generate distinct evolving temperature and polarization patterns in the CMB that can be tracked via Stokes parameters and potentially isolated per geometry.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Thurston spacetimes generate distinct time-evolving quadrupole patterns in CMB temperature and polarization via Stokes parameters.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9fbf81728ce4a9a4bbed8fb6fd3e259ebc30424f6f358958783f3bb682f1046c"},"source":{"id":"2605.14572","kind":"arxiv","version":1},"verdict":{"id":"58ec7cc7-f44b-42b9-ae0b-3fa7434f2033","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:22:07.838383Z","strongest_claim":"We show the evolution of temperature and polarization amplitudes in terms of such Stokes parameters at different timestamps and attempt to isolate individual Thurston geometries.","one_line_summary":"Thurston spacetimes generate distinct evolving temperature and polarization patterns in the CMB that can be tracked via Stokes parameters and potentially isolated per geometry.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That Thurston spacetimes can be used as viable background geometries for the universe while producing coherent, distinguishable CMB signals without additional assumptions about initial conditions or matter content in the anisotropic setting.","pith_extraction_headline":"Thurston spacetimes generate distinct time-evolving quadrupole patterns in CMB temperature and polarization via Stokes parameters."},"references":{"count":74,"sample":[{"doi":"","year":null,"title":"Solv These eight maximal geometries can be said to form the building blocks of all compact 3-manifolds and are referred to asThurston geometries. These are:","work_id":"dcc675d7-023b-474f-b6fe-b490815bd7bc","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"FLRW spacetimes R3/H3/S3 (3) ds2 =−dt 2 +a 2(t){dχ2 +S 2 κ(χ)dΩ2}(2.1)","work_id":"8182c246-4566-4826-b8aa-514b496654ab","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"FLRW spacetimes in 2D with a third flat anisotropic axis R×H 2/S2 (2) ds2 =−dt 2 +a 2(t){dz2 +dχ 2 +S 2 κ(χ)dϕ2}(2.2) {z∈R is orthogonal to (χ,ϕ) plane} where Sκ(χ) =    sin(χ√κ)√κ , κ >0 (S 3,","work_id":"33a81baf-2729-4a67-bf22-a1c880c89ce8","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Universal cover of the unit tangent bundle of the hyperbolic plane ^U(H2) (1) ds2 =−dt 2 +a 2(t) n dx2 + cosh2 x √ −κ dy2 + dz+ sinh x √ −κ dy 2o (2.5)","work_id":"73869e40-07a5-443e-b3f6-9cdf374f17eb","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Nilpotent subgroup of an extension of the group of isometries (abb.Nil)(1) ds2 =−dt 2 +a 2(t) dx2 + 1−κ x 2 dy2 +dz 2 −2x √ −κ dy dz (2.6)","work_id":"a1380242-2ca2-4e0c-8225-6edc38822189","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":74,"snapshot_sha256":"c55b7a46a86d4cbf7e8c2634d841c533264df29db70cf1cdd40c1607721ecfbb","internal_anchors":7},"formal_canon":{"evidence_count":1,"snapshot_sha256":"23746cf3666da0ce43056e9125ccf30ac3357b91bb6dedb2f4f1d16d0c7fa52b"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}